A small cage inside another larger cage, the bait, another Grey placed in the smaller cage, leave the door open on the larger cage and tie a string to the door and sit back and wait...
This will work if there is a exotic hanging around, or is the best way to catch the little one.
You really should report this to 911parrotalert, chances are the person that has lost the bird has also contacted 911parrotalert.
Knowing how it feels to loose a family member, I know for a fact any report of seeing a lost one provides much needed HOPE.
This old man climbed a tree, a very tall wet slimy tree, I couldn't make it all the way up to where our African Grey was perched, but close enough to make him fly, then the little creep just flew to another tree, a smaller tree, less slimy...

I almost reached out to grab him and away he went again, this time he went down to the ground, and Rose Ann was right there to get him.
We were very fortunate.
It might be the best thing to do by contacting 911parrotalert.
Here's the link...
911 Parrot Alert- Lost & Found Parrot & Bird database, Report a Lost Bird or Found Bird
Arty